Preheat the oven to 350. Grease and flour a 9x9 pan.
In a bowl combine the cake mix, melted butter, oil, and eggs. The batter should be very think, but bakes up incredibly moist. Reserve ⅓ cup of batter mixed with 2 tbsp of water for the topping, and spread the rest in to prepared baking dish.
For the cheesecake topping, beat cream cheese until like then add sugar until combined. Beat in egg until well blended, then add vanilla. Pour on top of brownie mixture and spread into an even layer.
Top cheesecake layers with dollops of the thinned out brownie batter and use a tooth pick or butter knife to make pretty swirls. Bake 20 - 25 minutes until toothpick inserted comes out clean.